Our cells multiply, by dividing in two. Cells in our body don’t live that long, so we are always making new cells to replace the old ones. When we grow our bones, it simply means more bones cells are being made than die. The big question is how does the body know where to make cells grow so that we grow taller and get older properly. Bones grow from the inside – the bone marrow in the centre of the bone is alive, and the outside is made of hard,dead cells.
It’s quite complicated how bones (and any other part of our body) grow– it is studied by people called Developmental Biologists. It’s not something I know very much about, but basically, we have genes that turn on and off at different times which control the patterns of cell growth. These ‘regulatory genes’ act like a conductor of an orchestra, deciding what instrument (cell type) needs to start and stop playing (multiplying) when and it directs them to multiply in a particular patterns (like a conductor gets a musician to follow a particular tune). Maybe one of the other scientists can explain more about the process than I can!